Back on the computer, I ordered a variable ND filter. Comprising two polarisers that darken considerably when their orientations are crossed (see video at the bottom), these filters are great when you want fine control over exposure in bright environments. As soon as it arrived I tried some experiments in my back yard.
|f/3.5 with variable ND filter|
|f/18 without filter|
One other noticable difference is the colour tone. With the filter, the picture looks cooler with a blue tint, and possibly desaturated. I have found with cheap ND filters that the optical quality is not perfect and colour shifts can occur, usually pushing towards blue. The effect varies with the severity of the light loss, and the quality of materials used -- one time I tried a plastic filter and the effect was something akin to picture taken with a Lomo/Diana toy camera, or something tweaked with Instagram. In the case of this variable ND filter, the colour shift is not so bad that it can't be corrected during editing.
A short video to demonstrate: